Incidence of electromagnetic waves on a plasma-vacuum boundary

An electromagnetic wave polarized in a plane normal to the magnetostatic field, parallel to the plasma boundary, falls from a vacuum on a half-space filled with magnetoactive plasma and bounded by a wall. The coefficient of wave reflection is computed for plasmas with ₀ ² / _h ² 1.The authors express their sincere thanks to Mr. J. Václavík for his discussions of the study.     

The extremal microscopic coherent boson states

In a recent paper, the Fock-normal (=microscopic) fully-coherent statesL _L ⁽⁾ (L denotes the factorizing linear form) have been completely characterized, and the existence of nonpure elements in the extreme boundary of the weak-*-compact, convex setL _L has been shown. This letter is devoted to an analysis of the extremal fully-coherent states, especially those which are not pure states. An affine isomorphism is constructed betweenL _L ⁽⁾ and a certain convex subset of the normal completely positive maps on the bounded operators on Fock space. Then the extreme boundary ofL _L ⁽⁾ is determined by results and techniques from the theory of completely positive operators.     

The Effect of Specular Reflectances on the Interaction of an Electromagnetic <Emphasis Type="Italic">E</Emphasis> Wave with a Thin Metal Film Placed between Two Dielectric Media

The interaction of an electromagnetic E wave with a thin metal film placed between two dielectric media is calculated in the case of different specular reflectances q₁ and q₂ for the reflection of electrons from the surface of the thin metal layer, in the case of variations in the values of dielectric permittivities ε₁ and ε₂ of the media, and in the case of different values of angle of incidence θ of the electromagnetic wave. The behavior of reflection coefficient R, transmission coefficient T, and absorption coefficient A in relation to the frequency of the external field is analyzed.     

Towards a generalized distribution formalism for gauge quantum fields

We prove that the distributions defined on the Gelfand-Shilov spacesS with < 1 and, hence, more singular than hyperfunctions, retain the angular localizability property. Specifically, they have uniquely determined support cones. This result enables one to develop a distribution-theoretic technique suitable for the consistent treatment of quantum fields with arbitrarily singular ultraviolet and infrared behavior. The proof covering the most general and difficult case = 0 is based on the use of the theory of plurisubharmonic functions and Hörmander'sL ²-estimates.This work was supported in part by a Soros Humanitarian Foundation Grant awarded by the American Physical Society.     

Computational Modelling and Experimental Investigation of Spin-Magnetoplasma Waves

The results of computational modelling of the reflection coefficient from the semiconductor surface under conditions of spin-magnetoplasma wave excitation on its surface with the simultaneous changing the concentration and the mobility of charge carriers as well as the relaxation time of magnetic subsystem are presented. The experiments were carried out on the unique automated measuring set-up with the attenuated total reflection technique. An accuracy of the temperature stabilization amounts to 0.1 in the temperature range T=4.2-300 . For the first time the surface spin-magnetoplasma waves were excited in the solid solutions of diluted magnetic semiconductors of Cd _1-x Mn _x Te and Hg _1-x-y Cd _x Mn _y Te types. The experimental results are in good agreement with numerical ones that allowed us to determine both the electron subsystem parameters on the semiconductor surface and the function describing their temperature law.     

Moduli spaces of curves and representation theory

We establish a canonical isomorphism between the second cohomology of the Lie algebra of regular differential operators on ^x of degree 1, and the second singular cohomology of the moduli space of quintuples (C, p, z, L, []), whereC is a smooth genusg Riemann surface,p a point onC, z a local parameter atp, L a degreeg–1 line bundle onC, and [] a class of local trivializations ofL atp which differ by a non-zero factor. The construction uses an interplay between various infinite-dimensional manifolds based on the topological spaceH of germs of holomorphic functions in a neighborhood of 0 in ^x and related topological spaces. The basic tool is a canonical map from to the infinite-dimensional Grassmannian of subspaces ofH, which is the orbit of the subspaceH _– of holomorphic functions on ^x vanishing at , under the group AutH. As an application, we give a Lie-algebraic proof of the Mumford formula: _n =(6n ²–6n+1)₁, where _n is the determinant line bundle of the vector bundle on the moduli space of curves of genusg, whose fiber overC is the space of differentials of degreen onC.     

Boson—Fermion Correspondence on the Circle via Quantum Stochastic Calculus

The quantum stochastic differential formula dB = (–1)dA, known to relateboson and fermion fields A and B, respectively, on the Fock space over L ²(R₊),is shown to hold in a modified form in a Fock space associated with the nontrivialcomplex line bundle over the circle S ¹.     

Superfocusing of a spherical wave: Theory and experiment

The possibility of focusing a spherical wave within a region considerably smaller than the wavelength is studied theoretically and experimentally. The coefficient of reflection of a spherical wave from a small rigid or soft sphere is-1. Consequently, the total field near such scatterers remains finite as the radius of the sphere tends to zero. The power of the acoustic field concentrates in this case in a region whose radius is proportional to the acoustic wavelength. The field can be enhanced by choosing an appropriate reflection coefficient. For example, if the reflection coefficient is made equal to 0, the sound pressure will be created by the converging wave alone. As the observation point approaches the center, this field increases without limit as 1/r, where r is the distance from the center. Structures that provide the absorption of the converging wave are analyzed. The experimental setup is described, and the experimental results demonstrating a strong absorption (the reflection coefficient does not exceed 0.2) of the converging wave are presented. The main result of the study is that it experimentally corroborates the possibility of focusing the wave in a region whose dimensions are much smaller than the wavelength.     

Generalized Bethe ansatz solution of a one-dimensional asymmetric exclusion process on a ring with blockage

We present a model for a one-dimensional anisotropic exclusion process describing particles moving deterministically on a ring of lengthL with a single defect, across which they move with probability 0 p 1. This model is equivalent to a two-dimensional, six-vertex model in an extreme anisotropic limit with a defect line interpolating between open and periodic boundary conditions. We solve this model with a Bethe ansatz generalized to this kind of boundary condition. We discuss in detail the steady state and derive exact expressions for the currentj, the density profilen(x), and the two-point density correlation function. In the thermodynamic limitL the phase diagram shows three phases, a low-density phase, a coexistence phase, and a high-density phase related to the low-density phase by a particle-hole symmetry. In the low-density phase the density profile decays exponentially with the distance from the boundary to its bulk value on a length scale . On the phase transition line diverges and the currentj approaches its critical valuej _c = p as a power law,j _c – j ^–1/2. In the coexistence phase the width of the interface between the high-density region and the low-density region is proportional toL ^1/2 if the density f 1/2 and=0 independent ofL if = 1/2. The (connected) two-point correlation function turns out to be of a scaling form with a space-dependent amplitude n(x₁, x₂) =A(x₂)A ^Ke^–r/ withr = x ₂ –x ₁ and a critical exponent = 0.     

Zum quantenmechanischen Vierkörperproblem

In a way similar to that of a former paper, the Schrödinger equation of the four-body problem has been transformed to appropriate coordinates. Besides those of the center of mass, these are the six distances between the four particles and the Eulerian angles describing the orientation of the instantaneous ellipsoid of inertia. By introduction of the angular momentum operatorsL _x″ ,L _y″ ,L _z″ the wave equation — in contrast to the more special three-body problem where the configuration needs must be plane — becomes fully symmetrical not only in the distances but also in these three operators. The solution can again be written as a linear combination of the eigenfunctionsD _MK ^L of the rigid rotator with coefficients depending upon the particle distances. The system of differential equations for these coefficient functions has been given; its behaviour under parity transformation turns out to be rather more involved than in the three-particle case.     

Correlation between the Soret coefficient and the static structure factor in a polymer blend

Mutual mass diffusion and thermal diffusion has been investigated in poly(dimethylsiloxane)/ poly(ethylmethylsiloxane) (PDMS/PEMS) polymer blends of equal weight fractions. Molar masses ranged from below 1 to over 20 kg/mol. Both the mutual mass (D) and the thermal diffusion (D_T) coefficient contain a thermally activated factor with an activation temperature of 1415 K. The molar mass dependence of D_T is due to an end-group effect of the local friction coefficient. The thermal diffusion coefficient in the limit of long chains and infinite temperature is D_T^0, = - 1.69×10^-7cm²(sK)^-1. The Soret coefficient S_T of blends far enough away from a critical point is proportional to the static structure factor S(q = 0).     

Expanding spherically symmetric models without shear

The integrability properties of the field equationL _xx =F(x)L ² of a spherically symmetric shear-free fluid are investigated. A first integral, subject to an integrability condition onF(x), is found, giving a new class of solutions which contains the solutions of Stephani and Srivastava as special cases. The integrability condition onF(x) is reduced to a quadrature which is expressible in terms of elliptic integrals in general. There are three classes of solution and in general the solution ofL _xx =F(x)L ² can only be written in parametric form. The case for whichF=F(x) can be explicitly given corresponds to the solution of Stephani. A Lie analysis ofL _xx =F(x)L ² is also performed. If a constant vanishes, then the solutions of Kustaanheimo and Qvist and of this paper are regained. For 0 we reduce the problem to a simpler, autonomous equation. The applicability of the Painlevé analysis is also briefly considered.     

Crossover finite-size scaling at first-order transitions

In a recent paper we developed a method which allows one to control rigorously the finite-size behavior in long cylinders near first-order phase transitions at low temperature. Here we apply this method to asymmetric transitions with two competing phases, and to theq-state Potts model as a typical model of a temperature-driven transition, whereq low-temperature phases compete with one high-temperature phase. We obtain the finite-size scaling of the firstN eigenvalues (whereN is the number of competing phases) of the transfer matrix in a periodic box of volumeL × ... ×L ×t, and, as a corollary, the finite-size scaling of the shape of the order parameter in a hypercubic box (t=L), the infinite cylinder (t=), and the crossover regime from hypercubic to cylindrical scaling. For the two-phase case (N=2 we find that the crossover length _L is given by O(L^w)exp(L^v), where is the inverse temperature, is the surface tension, and w=1/2 if v+1=2 whilew=0 if v+1 >2. For the standard Ising model we also consider free boundary conditions, showing that _L=exp[L^v+O(L^v– 1)] for any dimension v+12. For v+1=2 we finally discuss a class of boundary conditions which interpolate between free (corresponding to the interpolating parameter g=0) and periodic boundary conditions (corresponding to g=1), finding that _L=O(L^w)exp(L ^v) withw=0 forg=0 andw=1/2 for 0<g1.     

On the theory of eigenfunctions expansion of the Schrödinger operator

It is shown that the generalized eigenfunctions of the Schrödinger operator with singular potentials actins in L ₂(₃) are ordinary functions with determined asymptotic behaviour at infinity.     

Selective reflection from Rb vapor in half- and quarter-wave cells: Features and possible applications

The features of the effect of selective reflection from rubidium vapor in a nanocell with the thickness L ≈ λ/2 and L ≈ λ/4, where λ = 795 nm is the wavelength of laser radiation resonant with the Rb D₁ line, are studied. It is shown that, because of the behavior of the nanocell as a low-Q-factor Fabry–Pérot etalon, the sign of the derivative of the selective reflection spectra changes near L ≈ λ/2 from negative at L > λ/2 to positive at L < λ/2. The simplicity of the experimental implementation, large amplitude, and sub-Doppler width (40MHz) of a detected signal at an atomic transition frequency are appropriate for applications in metrology and magnetometry. In particular, selective reflection from the nanocell is a convenient frequency marker of atomic transitions; in this case, the amplitudes of peaks are proportional to the transition probabilities. The remote optical monitoring of a magnetic field with a spatial resolution L = λ/4 ≈ 199 of nm is possible on the basis of the splitting of selective reflection peaks in a strong magnetic field (up to 3 kG). A theoretical model describes well the experimental results.     

Special Features of the Reflection Coefficient in (Pb0.78Sn0.22)1–xInxTe (x = 0.05–0.20)

Spectral dependences of the reflection coefficient R are studied in solid solutions of (Pb_0.78Sn_0.22)_1–x In _x Te with indium content in the mixture x = 0.05–0.20 at T = 300 K. In the R() spectra of each of the examined specimens, two minima of the reflection coefficient are revealed: one in the short-wavelength region at = 1–2 m, and the other – in the long-wavelength region at = 25–30 m, the latter being due to plasma vibrations of free electrons. Peculiar features of the short-wavelength minima in the R() dependences are analyzed. It is shown that these minima are likely to be associated with heterogeneities formed by the nonuniform spatial distribution of indium in the specimen.     

Uniqueness and a priori bounds for certain homoclinic orbits of a Boussinesq system modelling solitary water waves

This paper establishes surprisingly precise a priori bounds on theL -norm of certain singular solutions of a system of two nonlinear Sturm-Liouville equations which model solitary water waves.These solutions can be interpreted as homoclinic orbits for a system of four first order ordinary differential equations. The uniqueness of these homoclinic orbits is established for certain choices of a parameterc, the phase speed of the waves. These observations do not result from perturbation of linear theory, but are global.     

A plane wave derivation of the Bragg acoustooptic equations and their application to the scattering of finite-width optical beams

The equations describing the interaction between an optical beam and an acoustic wave are derived using plane waves derived from elementary scattering sources. The results obtained are in good agreement with other well-known methods such as the differential difference equation approach. The equations are applied to the acousto-optic interaction in the weak and strong approximations and also to the scattering of finite-width optical beams with rectangular and Gaussian profiles. It is shown that in both cases the second or backscattered beam (A ₀) produces a substantial modification in the through beam (A ₀) resulting in an intensity null at some point in the beam profile. Equations are derived for the diffraction efficiency in finite-width beams and it is shown that in order to achieve maximum efficiencies it is essential to use small values of the parameter =L _B/W.     

The tangent bundle of a Calabi-Yau manifold-deformations and restriction to rational curves

The tangent bundle _X of a Calabi-Yau threefoldX is the only known example of a stable bundle with non-trivial restriction to any rational curve onX. By deforming the direct sum of _X and the trivial line bundle one can try to obtain new examples. We use algebro-geometric techniques to derive results in this direction. The relation to the finiteness of rational curves on Calabi-Yau threefolds is discussed.